Let's imagine (purely theoretically) that I'm William the Conqueror, and after having defeated the Anglo-Saxons I decided to buy a nice iron sword for myself. Of course, someone has to dig the ore out of the ground, but what happens next?
The main raw material needed for multiple steps is charcoal. This will be produced by a specialist charcoal burner. The charcoal burner works in the forest, where the wood is first cut and left to dry for a few months. Once the wood has dried, the logs are arranged in a large heap, and covered with turf (or dirt, moss, etc.). The pile is lit, and after about a week, the wood has been converted to charcoal by the heat driving out everything except the carbon. Some of the wood is burned in the process, to provide the required heat. Perhaps 4 tons of wood might be used to produce 1 ton of charcoal (4 tons of wood would be a small charcoal pile).
Logs being piled for charcoal making: https://en.wikipedia.org/wiki/File:Köhlerei_in_Grünburg.jpg
Examples of charcoal piles, including covered piles: https://en.wikipedia.org/wiki/Charcoal_pile
The other raw material needed is iron ore. A major source of iron ore was bog iron. Other iron ores might be used too, depending on local availability. Iron smelting at the time was very small scale compared to modern iron production, and many ore sources that were sufficient for local iron production in the High Middle Ages would not be economically usable today. The ore is collected, washed, and roasted. The roasting drives out some impurities, and converts hydrated iron oxides to anhydrous iron oxides. After roasting, the ore is broken into small pieces if necessary.
The next step is smelting, the conversion of ore to metal. This would be done in a bloomery furnace, as used since the early Iron Age. The High Middle Ages is before the late Medieval growth in bloomery sizes and the introduction of the blast-bloomery (a blast furnace designed to produce a bloom as its product rather than cast iron). Charcoal and the roasted iron are are piled in layers in the furnace, using perhaps 20-50kg of ore and 30-80kg of charcoal, and the charcoal is lit. (The furnace might be preheated first by burning charcoal in it, before it is charged with the ore+charcoal.) The charcoal performs 3 functions:
It is the fuel for the process, being burnt to increase the temperature to over 1200C.
To convert the iron ore (iron oxide) into metallic iron, the oxygen chemically bonded to the iron must be removed. This is done by getting the oxygen to bond to carbon instead - the charcoal is the source of the carbon.
Steel is iron with carbon (say, 0.2% to 2% carbon) dissolved in it. The charcoal is the source of this carbon. The diffusion of carbon into the iron is slow, and can be sped up by higher temperatures. To increase the yield and quality of steel in the smelting process, the furnace is raised to a higher temperature, and kept at that temperature for some time (much longer than needed simply to convert the ore to metal).
This smelting process all happens in the solid state - the temperatures, while high, are not high enough to melt iron or steel. The product is a bloom, a spongy inhomogeneous mass of iron, steel, and slag. The slag is removed from the furnace while hot, and consolidated, beaten with a hammer (often a large wooden hammer) to compress it and expel slag. A large bloom will be broken into smaller pieces for future forging of iron/steel objects. The carbon content varies in the bloom, and the pieces can be sorted for different iron content.
The next step is forging the sword blade. The swordsmith will buy iron and/or steel, and charcoal. The sword would typically have an iron or low carbon steel body, with high carbon steel cutting edges (ideally, about 0.6-0.8% carbon) welded on (a higher quality sword), or might be made entirely or low/medium carbon steel (a lower quality sword). By William's time, decorative pattern welding had largely fallen out of use.
The swordsmith chooses the iron and steel, and repeatedly hammers out, folds, and welds the pieces to reduce the slag content and obtain homogeneous pieces of iron or steel of a suitable size. These will then be welded together, to produce the iron/steel body and steel cutting edges, and forged into the shape of the sword blade. If the blade has an iron inlay, it will be done at this time. The smith will then file/grind the sword to close to the final blade shape. The blade will then, for a good quality sword, be quenched to harden it - the blade is heated, and then plunged into water to quickly cool it. The sword is usually pulled from the quenching water before it is fully cooled, so that the residual heat can temper it - reduce the hardness a little bit, and reduce the brittleness a lot (steel that has been completely quenched without being tempered is very hard, but brittle). A low quality sword might not be quenched. The laminated/composite construction, with high carbon steel edges and iron/lower-carbon-steel body helps reduce the importance of tempering: if the hard high carbon edge cracks, the softer but tougher body of the sword will hold things together.
For forging and welding, the iron needs to be hot (red/yellow hot!). The heat source used for this (and for heating the blade for quenching) is charcoal. The charcoal burner makes a contribution here too.
The high carbon steel cutting edges might, after quenching and tempering, have a hardness in the range of 250-500HV (25-50HRC). Unquenched blades might have hardnesses of about 200HV.
Next, the blade will be sharpened and polished. If the blade has a copper alloy (latten) or silver inlay, it will be done at this time.
Next the blade will be fitted with a guard (usually iron) and pommel (usually iron), and grip. This will often be done by a specialist cutler, rather than the swordsmith.
Next, a scabbard will be made for the sword. The scabbard will have a thin wooden core, and be covered with linen and/or thin leather (if both, linen first, then leather). This composite construction results in a light and strong scabbard. Metal fittings might be used to reinforce the tip and mouth of the scabbard, and for decorative purposes, too. The scabbard might be painted, or the leather tooled, for decoration.
Now, William has his sword!